Response to a Small-Signal Stimulus in the Frequency Domain

3 Response to a Small-Signal Stimulus in the Frequency Domain 

A monochromatic signal v(f) = VmSin((Ot), involving the single frequency v = (oUk, is applied to a cell and the resulting steady state current i(t) = 7 sin(ft)t + 9) meas- 

Impedance may be defined not only for discrete systems but also for arbitrary distributed systems as the Fourier transform of the differential equation defining the voltage response divided by the Fourier transform of the periodic current excitation Z( (d) = F v t) F i t). Here the F operator denotes a Fourier transform. However, Fourier transformation only reduces differential equations to simple Ohm s law-like form under conditions of linearity, causality, and stationarity of the system therefore impedance is properly defined only for systems satisfying these conditions. 

In general, Z is frequency-dependent, as defined above. Conventional IS consists of the (nowadays often automated) measurement of Z as a function of v or over a wide frequency range. It is from the resulting structure of the Z( ) vs. response that one derives information about the electrical properties of the full electrode-material system. 

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